Here are listed all the ways the current script are enabling factions to change names as time passes. Feel free to both suggest new ones, and how the current ones are used, in the mod comments section! :)

This enables faction names to change as your legendary lord ranks up. Excellent for example horde factions or factions focused more on a character than the actual faction.

• Example:
  Playing as Archaon. Your faction name will become Swords of Chaos (Archaons personal horde) But as you rank up, your faction name will more and more show how he truly is the herald of the Apocalypse.
  
  Rank 10 - The Slayers of Kings
  Rank 20 - Scourge of the World
  Rank 30 - Heralds of the Endtimes
  Rank 40 - Chaos Undivided

This is the vanilla CA script mechanic that's been improved on and with the added part that also can be a set of provinces in general. Meaning own 2 provinces (no matter which) for example.

Making it possible for faction name changes to happen once taken over a pre-set list of provinces.

• Example:
  Playing as Emperor Karl Franz, your faction starts off as the City State of Altdorf. Then changing to Grand Principality of Reikland when finally taken back all of Reikland from the rebels. And into Empire of Man once control the entire empire!
  
  Lastly becoming The Greater Sigmarite Imperium once taken over all of the realms of human factions.

This script addition enables faction names to change simply based on how many regions they control! Not being tied down to a pre-set loreful list of provinces. Excellent for example greenskin factions. Who now are free to rampage in whatever direction they desire!

• Example:
  Playing as Grimgor, your tribe status raises up to being Da Great WAAAGH! once taken over 15 regions. Then Da Prophesied WAAAGH! once controlling 30 regions. And lastly Da Green Tide! once control 60 regions. Wherever on the map!

You're the last faction left on the map in your race culture? Then your name can change!

• Example:
  Playing as a high elves faction, your faction name will change to the Phoenix Kingdom if you're the only high elf faction left standing.

Very similar to no.1 on this list, this one simply narrows it more down. Making so a faction only needs to take over a precise region(s) instead of the hole province they each belong to.

• Example:
  Playig as Belegar, just having to take over Karak Eight-Peaks region, not its entire province.

A region have a really important meaning to an legendary lord? In the sense they want to raze it rather than own it? Then this script are for that!

We are always looking for new interesting ways to make the faction name changes happen as you play! Also always open for ideas from all of you! :) So got an idea for a way that would be interesting, cool or practical in how faction names changes? Then feel free to share it with us in the comment section!

Looking forward to be hearing from you